What happens: when running synchronization the used Outook Exchange Mailbox (the online one, that's the matter) does not in fact sync with device.
Looking at configuration I found this: the mapped folder is not the Exchange Mailbox, but another offline, personal folder.

I tried all of this, after uninstall BDS and install again:

_ start with Outlook with no any personal folder opened, only the Exchange one. In this case when you try to configure the Organizer on Calendar, MemoPad, Address Book and Tasks application you can't. You follow the steps and in the end the app is not selected;

_ start with some personal .pst Outlook opened. In this case the folders Calendar, Contacts, Notes and Tasks on this personal .pst folder is created and the sync happens on these folders at first time. THE PROBLEM is that after first sync operation there's no real synchronization: you add some item on device and this does not goes to online Exchange .ost folder and vice-versa.

If you try to map to the Exchange folder:

organizer -> Configure settings -> Advanced -> Map Folder

You cannot and get the error message on the title of this post: 0x80043bea